The Brauer group and the center of generic matrices

DOI10.1016/0021-8693(85)90073-0zbMath0586.13005OpenAlexW2033044203MaRDI QIDQ1071819

David J. Saltman

Publication date: 1985

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-8693(85)90073-0

zbMATH Keywords

Brauer groupBrauer-Severi varietygeneric matricesunirational fields

Mathematics Subject Classification ID

Galois cohomology (12G05) Rational and unirational varieties (14M20) Brauer groups of schemes (14F22) Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) (16H05) Division rings and semisimple Artin rings (16Kxx) Rings with polynomial identity (16Rxx)

Related Items (20)

Principal homogeneous spaces under flasque tori; applications ⋮ Multiplicative field invariants ⋮ Dubrovin valuation rings and Henselization ⋮ Excellent algebraic groups. I ⋮ Birational classification of fields of invariants for groups of order 128 ⋮ The Bogomolov multiplier of rigid finite groups ⋮ Stable rationality of certain \(PGL_ n\)-quotients ⋮ Centers of generic division algebras, the rationality problem 1965-1990 ⋮ Brauer Group and Birational Type of Moduli Spaces of Torsionfree Sheaves on a Nodal Curve ⋮ Open problems on central simple algebras. ⋮ Division algebras over Henselian fields. ⋮ Cohomology of certain moduli spaces of vector bundles ⋮ Birational geometry of linear algebraic groups and Galois modules ⋮ Specializations of Brauer classes over algebraic function fields ⋮ The Brauer group of an affine cone ⋮ Four-fold Massey products in Galois cohomology ⋮ Degree three unramified cohomology groups and Noether's problem for groups of order 243 ⋮ Rationality problems and conjectures of Milnor and Bloch–Kato ⋮ The Schur index and Moody's theorem ⋮ Unramified cohomology of classifying varieties for classical simply connected groups1

Cites Work

• Generic splitting fields of central simple algebras
• Retract rational fields and cyclic Galois extensions
• Invariants and the ring of generic matrices
• A cohomological interpretation of Brauer groups of rings
• Rational functions invariant under a finite Abelian group
• PI-algebras. An introduction
• Separable algebras over commutative rings
• On the Galois cohomology of the projective linear group and its applications to the construction of generic splitting fields of algebras
• The Brauer Group of a Commutative Ring
• The polynomial identities of matrices
• Generic splitting fields
• Some Elementary Examples of Unirational Varieties Which are Not Rational
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